Here’s an actual formula, as developed by Don Luymes, the Manager of Community Planning for the City of Surrey:
An economically, socially and environmentally healthy (or sustainable) city is usually marked by economic growth exceeding population growth exceeding urban area growth (E>P>U).
In my thinking to date, economic growth is most easily measured by the increase in total value of assessed land and improvements over a certain period, population growth is measured over that same period, and urban area growth is most easily measured as the increase in area covered by sanitary sewer service in that same period (urban growth can also be measured by capturing all development above a certain density, but this gets very messy when dealing with various industrial uses).
As an example, if the total assessed value of a city increased by 4% per year, while population growth was 2% per year and the urban area expanded by 1% per year, this is likely a city that is relatively healthy: incomes/wealth per capita is likely being created (E>P) and overall density is also increasing (P>U). Good things can happen when taxable wealth is created and geographically concentrated and when density is concurrently increased – things like jobs, public realm improvements, transit investments etc etc.
Of course, there are many exceptions and much complexity (I’ll write a book about it someday), but that is the gist of it.